Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 38 :  Second derivative test for local maxima / minima & saddle points [Section 38.1]
38 .1 Second derivative test for local maxima/minima and saddle points
  In order to obtain sufficient conditions for local maxima, local minima and saddle points, we need the following notion.
   
38.1.1 Definition
 

Let and be an interior point. Let all the second order partial derivatives of at exist. Then

is called the discriminant (or hessian) of at .

   
38.1.2

Note:

 

If

then

For example, this would be the case if and are continuous at Further, in such a case, if , then both and are nonzero and have the same sign.

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